The Congruences of a Finite Lattice: A Proof-by-Picture Approach by George Grätzer

by George Grätzer

The congruences of a lattice form the congruence lattice. In the past half-century, the study of congruence lattices has become a large and important field with a great number of interesting and deep results and many open problems. This self-contained exposition by one of the leading experts in lattice theory, George Grätzer, presents the major results on congruence lattices of finite lattices featuring the author's signature "Proof-by-Picture" method and its conversion to transparencies.Key * Includes the latest findings from a pioneering researcher in the field* Insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions* Contains complete proofs, an extensive bibliography and index, and nearly 80 open problems* Additional information provided by the author online The book is appropriate for a one-semester graduate course in lattice theory, yet is also designed as a practical reference for researchers studying lattices.

Hardcover

First published November 9, 2005